1,967 research outputs found
Reasoning about Minimal Belief and Negation as Failure
We investigate the problem of reasoning in the propositional fragment of
MBNF, the logic of minimal belief and negation as failure introduced by
Lifschitz, which can be considered as a unifying framework for several
nonmonotonic formalisms, including default logic, autoepistemic logic,
circumscription, epistemic queries, and logic programming. We characterize the
complexity and provide algorithms for reasoning in propositional MBNF. In
particular, we show that entailment in propositional MBNF lies at the third
level of the polynomial hierarchy, hence it is harder than reasoning in all the
above mentioned propositional formalisms for nonmonotonic reasoning. We also
prove the exact correspondence between negation as failure in MBNF and negative
introspection in Moore's autoepistemic logic
Implementing Default and Autoepistemic Logics via the Logic of GK
The logic of knowledge and justified assumptions, also known as logic of
grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for
nonmonotonic reasoning. To date, it has been used to embed in it default logic
(propositional case), autoepistemic logic, Turner's logic of universal
causation, and general logic programming under stable model semantics. Besides
showing the generality of GK as a logic for nonmonotonic reasoning, these
embeddings shed light on the relationships among these other logics. In this
paper, for the first time, we show how the logic of GK can be embedded into
disjunctive logic programming in a polynomial but non-modular translation with
new variables. The result can then be used to compute the extension/expansion
semantics of default logic, autoepistemic logic and Turner's logic of universal
causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic
Reasoning (NMR 2014
Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence
Recently, it has been shown that probabilistic entailment under coherence is
weaker than model-theoretic probabilistic entailment. Moreover, probabilistic
entailment under coherence is a generalization of default entailment in System
P. In this paper, we continue this line of research by presenting probabilistic
generalizations of more sophisticated notions of classical default entailment
that lie between model-theoretic probabilistic entailment and probabilistic
entailment under coherence. That is, the new formalisms properly generalize
their counterparts in classical default reasoning, they are weaker than
model-theoretic probabilistic entailment, and they are stronger than
probabilistic entailment under coherence. The new formalisms are useful
especially for handling probabilistic inconsistencies related to conditioning
on zero events. They can also be applied for probabilistic belief revision.
More generally, in the same spirit as a similar previous paper, this paper
sheds light on exciting new formalisms for probabilistic reasoning beyond the
well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on
Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks
in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200
On Properties of Update Sequences Based on Causal Rejection
We consider an approach to update nonmonotonic knowledge bases represented as
extended logic programs under answer set semantics. New information is
incorporated into the current knowledge base subject to a causal rejection
principle enforcing that, in case of conflicts, more recent rules are preferred
and older rules are overridden. Such a rejection principle is also exploited in
other approaches to update logic programs, e.g., in dynamic logic programming
by Alferes et al. We give a thorough analysis of properties of our approach, to
get a better understanding of the causal rejection principle. We review
postulates for update and revision operators from the area of theory change and
nonmonotonic reasoning, and some new properties are considered as well. We then
consider refinements of our semantics which incorporate a notion of minimality
of change. As well, we investigate the relationship to other approaches,
showing that our approach is semantically equivalent to inheritance programs by
Buccafurri et al. and that it coincides with certain classes of dynamic logic
programs, for which we provide characterizations in terms of graph conditions.
Therefore, most of our results about properties of causal rejection principle
apply to these approaches as well. Finally, we deal with computational
complexity of our approach, and outline how the update semantics and its
refinements can be implemented on top of existing logic programming engines.Comment: 59 pages, 2 figures, 3 tables, to be published in "Theory and
Practice of Logic Programming
Embedding Defeasible Logic into Logic Programming
Defeasible reasoning is a simple but efficient approach to nonmonotonic
reasoning that has recently attracted considerable interest and that has found
various applications. Defeasible logic and its variants are an important family
of defeasible reasoning methods. So far no relationship has been established
between defeasible logic and mainstream nonmonotonic reasoning approaches.
In this paper we establish close links to known semantics of logic programs.
In particular, we give a translation of a defeasible theory D into a
meta-program P(D). We show that under a condition of decisiveness, the
defeasible consequences of D correspond exactly to the sceptical conclusions of
P(D) under the stable model semantics. Without decisiveness, the result holds
only in one direction (all defeasible consequences of D are included in all
stable models of P(D)). If we wish a complete embedding for the general case,
we need to use the Kunen semantics of P(D), instead.Comment: To appear in Theory and Practice of Logic Programmin
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